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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    <a name="line.17"></a>
<FONT color="green">018</FONT>    package org.apache.commons.math3.analysis.solvers;<a name="line.18"></a>
<FONT color="green">019</FONT>    <a name="line.19"></a>
<FONT color="green">020</FONT>    /**<a name="line.20"></a>
<FONT color="green">021</FONT>     * Implements the &lt;em&gt;Regula Falsi&lt;/em&gt; or &lt;em&gt;False position&lt;/em&gt; method for<a name="line.21"></a>
<FONT color="green">022</FONT>     * root-finding (approximating a zero of a univariate real function). It is a<a name="line.22"></a>
<FONT color="green">023</FONT>     * modified {@link SecantSolver &lt;em&gt;Secant&lt;/em&gt;} method.<a name="line.23"></a>
<FONT color="green">024</FONT>     *<a name="line.24"></a>
<FONT color="green">025</FONT>     * &lt;p&gt;The &lt;em&gt;Regula Falsi&lt;/em&gt; method is included for completeness, for<a name="line.25"></a>
<FONT color="green">026</FONT>     * testing purposes, for educational purposes, for comparison to other<a name="line.26"></a>
<FONT color="green">027</FONT>     * algorithms, etc. It is however &lt;strong&gt;not&lt;/strong&gt; intended to be used<a name="line.27"></a>
<FONT color="green">028</FONT>     * for actual problems, as one of the bounds often remains fixed, resulting<a name="line.28"></a>
<FONT color="green">029</FONT>     * in very slow convergence. Instead, one of the well-known modified<a name="line.29"></a>
<FONT color="green">030</FONT>     * &lt;em&gt;Regula Falsi&lt;/em&gt; algorithms can be used ({@link IllinoisSolver<a name="line.30"></a>
<FONT color="green">031</FONT>     * &lt;em&gt;Illinois&lt;/em&gt;} or {@link PegasusSolver &lt;em&gt;Pegasus&lt;/em&gt;}). These two<a name="line.31"></a>
<FONT color="green">032</FONT>     * algorithms solve the fundamental issues of the original &lt;em&gt;Regula<a name="line.32"></a>
<FONT color="green">033</FONT>     * Falsi&lt;/em&gt; algorithm, and greatly out-performs it for most, if not all,<a name="line.33"></a>
<FONT color="green">034</FONT>     * (practical) functions.<a name="line.34"></a>
<FONT color="green">035</FONT>     *<a name="line.35"></a>
<FONT color="green">036</FONT>     * &lt;p&gt;Unlike the &lt;em&gt;Secant&lt;/em&gt; method, the &lt;em&gt;Regula Falsi&lt;/em&gt; guarantees<a name="line.36"></a>
<FONT color="green">037</FONT>     * convergence, by maintaining a bracketed solution. Note however, that due to<a name="line.37"></a>
<FONT color="green">038</FONT>     * the finite/limited precision of Java's {@link Double double} type, which is<a name="line.38"></a>
<FONT color="green">039</FONT>     * used in this implementation, the algorithm may get stuck in a situation<a name="line.39"></a>
<FONT color="green">040</FONT>     * where it no longer makes any progress. Such cases are detected and result<a name="line.40"></a>
<FONT color="green">041</FONT>     * in a {@code ConvergenceException} exception being thrown. In other words,<a name="line.41"></a>
<FONT color="green">042</FONT>     * the algorithm theoretically guarantees convergence, but the implementation<a name="line.42"></a>
<FONT color="green">043</FONT>     * does not.&lt;/p&gt;<a name="line.43"></a>
<FONT color="green">044</FONT>     *<a name="line.44"></a>
<FONT color="green">045</FONT>     * &lt;p&gt;The &lt;em&gt;Regula Falsi&lt;/em&gt; method assumes that the function is continuous,<a name="line.45"></a>
<FONT color="green">046</FONT>     * but not necessarily smooth.&lt;/p&gt;<a name="line.46"></a>
<FONT color="green">047</FONT>     *<a name="line.47"></a>
<FONT color="green">048</FONT>     * &lt;p&gt;Implementation based on the following article: M. Dowell and P. Jarratt,<a name="line.48"></a>
<FONT color="green">049</FONT>     * &lt;em&gt;A modified regula falsi method for computing the root of an<a name="line.49"></a>
<FONT color="green">050</FONT>     * equation&lt;/em&gt;, BIT Numerical Mathematics, volume 11, number 2,<a name="line.50"></a>
<FONT color="green">051</FONT>     * pages 168-174, Springer, 1971.&lt;/p&gt;<a name="line.51"></a>
<FONT color="green">052</FONT>     *<a name="line.52"></a>
<FONT color="green">053</FONT>     * @since 3.0<a name="line.53"></a>
<FONT color="green">054</FONT>     * @version $Id: RegulaFalsiSolver.java 1364387 2012-07-22 18:14:11Z tn $<a name="line.54"></a>
<FONT color="green">055</FONT>     */<a name="line.55"></a>
<FONT color="green">056</FONT>    public class RegulaFalsiSolver extends BaseSecantSolver {<a name="line.56"></a>
<FONT color="green">057</FONT>    <a name="line.57"></a>
<FONT color="green">058</FONT>        /** Construct a solver with default accuracy (1e-6). */<a name="line.58"></a>
<FONT color="green">059</FONT>        public RegulaFalsiSolver() {<a name="line.59"></a>
<FONT color="green">060</FONT>            super(DEFAULT_ABSOLUTE_ACCURACY, Method.REGULA_FALSI);<a name="line.60"></a>
<FONT color="green">061</FONT>        }<a name="line.61"></a>
<FONT color="green">062</FONT>    <a name="line.62"></a>
<FONT color="green">063</FONT>        /**<a name="line.63"></a>
<FONT color="green">064</FONT>         * Construct a solver.<a name="line.64"></a>
<FONT color="green">065</FONT>         *<a name="line.65"></a>
<FONT color="green">066</FONT>         * @param absoluteAccuracy Absolute accuracy.<a name="line.66"></a>
<FONT color="green">067</FONT>         */<a name="line.67"></a>
<FONT color="green">068</FONT>        public RegulaFalsiSolver(final double absoluteAccuracy) {<a name="line.68"></a>
<FONT color="green">069</FONT>            super(absoluteAccuracy, Method.REGULA_FALSI);<a name="line.69"></a>
<FONT color="green">070</FONT>        }<a name="line.70"></a>
<FONT color="green">071</FONT>    <a name="line.71"></a>
<FONT color="green">072</FONT>        /**<a name="line.72"></a>
<FONT color="green">073</FONT>         * Construct a solver.<a name="line.73"></a>
<FONT color="green">074</FONT>         *<a name="line.74"></a>
<FONT color="green">075</FONT>         * @param relativeAccuracy Relative accuracy.<a name="line.75"></a>
<FONT color="green">076</FONT>         * @param absoluteAccuracy Absolute accuracy.<a name="line.76"></a>
<FONT color="green">077</FONT>         */<a name="line.77"></a>
<FONT color="green">078</FONT>        public RegulaFalsiSolver(final double relativeAccuracy,<a name="line.78"></a>
<FONT color="green">079</FONT>                                 final double absoluteAccuracy) {<a name="line.79"></a>
<FONT color="green">080</FONT>            super(relativeAccuracy, absoluteAccuracy, Method.REGULA_FALSI);<a name="line.80"></a>
<FONT color="green">081</FONT>        }<a name="line.81"></a>
<FONT color="green">082</FONT>    <a name="line.82"></a>
<FONT color="green">083</FONT>        /**<a name="line.83"></a>
<FONT color="green">084</FONT>         * Construct a solver.<a name="line.84"></a>
<FONT color="green">085</FONT>         *<a name="line.85"></a>
<FONT color="green">086</FONT>         * @param relativeAccuracy Relative accuracy.<a name="line.86"></a>
<FONT color="green">087</FONT>         * @param absoluteAccuracy Absolute accuracy.<a name="line.87"></a>
<FONT color="green">088</FONT>         * @param functionValueAccuracy Maximum function value error.<a name="line.88"></a>
<FONT color="green">089</FONT>         */<a name="line.89"></a>
<FONT color="green">090</FONT>        public RegulaFalsiSolver(final double relativeAccuracy,<a name="line.90"></a>
<FONT color="green">091</FONT>                                 final double absoluteAccuracy,<a name="line.91"></a>
<FONT color="green">092</FONT>                                 final double functionValueAccuracy) {<a name="line.92"></a>
<FONT color="green">093</FONT>            super(relativeAccuracy, absoluteAccuracy, functionValueAccuracy, Method.REGULA_FALSI);<a name="line.93"></a>
<FONT color="green">094</FONT>        }<a name="line.94"></a>
<FONT color="green">095</FONT>    }<a name="line.95"></a>




























































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